New Primal-Dual Weak Galerkin Finite Element Methods for Convection-Diffusion Problems

TL;DR

This paper introduces a novel primal-dual weak Galerkin finite element method for convection-diffusion equations, providing optimal error estimates and validating them through numerical experiments.

Contribution

It develops a new primal-dual weak Galerkin method with proven optimal error estimates for convection-diffusion problems.

Findings

Optimal error estimates in various norms

Numerical experiments confirm theoretical results

Method effectively solves convection-diffusion equations

Abstract

This article devises a new primal-dual weak Galerkin finite element method for the convection-diffusion equation. Optimal order error estimates are established for the primal-dual weak Galerkin approximations in various discrete norms and the standard $L^2$ norms. A series of numerical experiments are conducted and reported to verify the theoretical findings.